LMFDB - Embedded newform 2303.4.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,4,Mod(1,2303)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2303.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2303.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$135.881398743$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	2303.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.14945 q^{2} +8.07223 q^{3} +9.21794 q^{4} +8.04659 q^{5} -33.4953 q^{6} -5.05376 q^{8} +38.1609 q^{9} +O(q^{10})$	\(q-4.14945 q^{2} +8.07223 q^{3} +9.21794 q^{4} +8.04659 q^{5} -33.4953 q^{6} -5.05376 q^{8} +38.1609 q^{9} -33.3889 q^{10} -44.2783 q^{11} +74.4093 q^{12} -63.9904 q^{13} +64.9539 q^{15} -52.7732 q^{16} +27.0207 q^{17} -158.347 q^{18} +49.5156 q^{19} +74.1729 q^{20} +183.731 q^{22} +210.101 q^{23} -40.7951 q^{24} -60.2524 q^{25} +265.525 q^{26} +90.0935 q^{27} +100.554 q^{29} -269.523 q^{30} -58.2624 q^{31} +259.410 q^{32} -357.425 q^{33} -112.121 q^{34} +351.765 q^{36} -305.478 q^{37} -205.462 q^{38} -516.545 q^{39} -40.6655 q^{40} +415.627 q^{41} -139.779 q^{43} -408.154 q^{44} +307.065 q^{45} -871.803 q^{46} +47.0000 q^{47} -425.997 q^{48} +250.015 q^{50} +218.117 q^{51} -589.859 q^{52} +192.720 q^{53} -373.838 q^{54} -356.289 q^{55} +399.701 q^{57} -417.244 q^{58} +679.573 q^{59} +598.741 q^{60} -493.348 q^{61} +241.757 q^{62} -654.222 q^{64} -514.904 q^{65} +1483.12 q^{66} +14.9318 q^{67} +249.075 q^{68} +1695.98 q^{69} -250.816 q^{71} -192.856 q^{72} +1231.66 q^{73} +1267.57 q^{74} -486.372 q^{75} +456.431 q^{76} +2143.38 q^{78} -21.2513 q^{79} -424.644 q^{80} -303.089 q^{81} -1724.63 q^{82} -400.284 q^{83} +217.424 q^{85} +580.007 q^{86} +811.695 q^{87} +223.772 q^{88} +298.970 q^{89} -1274.15 q^{90} +1936.70 q^{92} -470.308 q^{93} -195.024 q^{94} +398.431 q^{95} +2094.01 q^{96} +218.811 q^{97} -1689.70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) $ 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.14945	−1.46705	−0.733526	−	0.679661i	$-0.762127\pi$
$2$	−4.14945	−1.46705	−0.733526	+	0.679661i	$0.762127\pi$
$3$	8.07223	1.55350	0.776751	−	0.629808i	$-0.216866\pi$
$3$	8.07223	1.55350	0.776751	+	0.629808i	$0.216866\pi$
$4$	9.21794	1.15224
$5$	8.04659	0.719709	0.359854	−	0.933009i	$-0.382826\pi$
$5$	8.04659	0.719709	0.359854	+	0.933009i	$0.382826\pi$
$6$	−33.4953	−2.27907
$7$	0	0
$7$	0	0
$8$	−5.05376	−0.223347
$9$	38.1609	1.41337
$10$	−33.3889	−1.05585
$11$	−44.2783	−1.21367	−0.606837	−	0.794826i	$-0.707562\pi$
$11$	−44.2783	−1.21367	−0.606837	+	0.794826i	$0.707562\pi$
$12$	74.4093	1.79001
$13$	−63.9904	−1.36521	−0.682605	−	0.730787i	$-0.739153\pi$
$13$	−63.9904	−1.36521	−0.682605	+	0.730787i	$0.739153\pi$
$14$	0	0
$15$	64.9539	1.11807
$16$	−52.7732	−0.824581
$17$	27.0207	0.385498	0.192749	−	0.981248i	$-0.438260\pi$
$17$	27.0207	0.385498	0.192749	+	0.981248i	$0.438260\pi$
$18$	−158.347	−2.07348
$19$	49.5156	0.597877	0.298938	−	0.954272i	$-0.403368\pi$
$19$	49.5156	0.597877	0.298938	+	0.954272i	$0.403368\pi$
$20$	74.1729	0.829278
$21$	0	0
$22$	183.731	1.78052
$23$	210.101	1.90474	0.952371	−	0.304942i	$-0.0986371\pi$
$23$	210.101	1.90474	0.952371	+	0.304942i	$0.0986371\pi$
$24$	−40.7951	−0.346970
$25$	−60.2524	−0.482020
$26$	265.525	2.00283
$27$	90.0935	0.642167
$28$	0	0
$29$	100.554	0.643876	0.321938	−	0.946761i	$-0.395666\pi$
$29$	100.554	0.643876	0.321938	+	0.946761i	$0.395666\pi$
$30$	−269.523	−1.64026
$31$	−58.2624	−0.337556	−0.168778	−	0.985654i	$-0.553982\pi$
$31$	−58.2624	−0.337556	−0.168778	+	0.985654i	$0.553982\pi$
$32$	259.410	1.43305
$33$	−357.425	−1.88544
$34$	−112.121	−0.565546
$35$	0	0
$36$	351.765	1.62854
$37$	−305.478	−1.35730	−0.678652	−	0.734460i	$-0.737436\pi$
$37$	−305.478	−1.35730	−0.678652	+	0.734460i	$0.737436\pi$
$38$	−205.462	−0.877116
$39$	−516.545	−2.12086
$40$	−40.6655	−0.160745
$41$	415.627	1.58317	0.791586	−	0.611057i	$-0.209255\pi$
$41$	415.627	1.58317	0.791586	+	0.611057i	$0.209255\pi$
$42$	0	0
$43$	−139.779	−0.495724	−0.247862	−	0.968795i	$-0.579728\pi$
$43$	−139.779	−0.495724	−0.247862	+	0.968795i	$0.579728\pi$
$44$	−408.154	−1.39845
$45$	307.065	1.01721
$46$	−871.803	−2.79436
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	−425.997	−1.28099
$49$	0	0
$50$	250.015	0.707148
$51$	218.117	0.598872
$52$	−589.859	−1.57305
$53$	192.720	0.499473	0.249737	−	0.968314i	$-0.419656\pi$
$53$	192.720	0.499473	0.249737	+	0.968314i	$0.419656\pi$
$54$	−373.838	−0.942092
$55$	−356.289	−0.873491
$56$	0	0
$57$	399.701	0.928802
$58$	−417.244	−0.944599
$59$	679.573	1.49954	0.749770	−	0.661699i	$-0.230164\pi$
$59$	679.573	1.49954	0.749770	+	0.661699i	$0.230164\pi$
$60$	598.741	1.28829
$61$	−493.348	−1.03552	−0.517760	−	0.855526i	$-0.673234\pi$
$61$	−493.348	−1.03552	−0.517760	+	0.855526i	$0.673234\pi$
$62$	241.757	0.495212
$63$	0	0
$64$	−654.222	−1.27778
$65$	−514.904	−0.982554
$66$	1483.12	2.76604
$67$	14.9318	0.0272269	0.0136135	−	0.999907i	$-0.495667\pi$
$67$	14.9318	0.0272269	0.0136135	+	0.999907i	$0.495667\pi$
$68$	249.075	0.444187
$69$	1695.98	2.95902
$70$	0	0
$71$	−250.816	−0.419244	−0.209622	−	0.977782i	$-0.567223\pi$
$71$	−250.816	−0.419244	−0.209622	+	0.977782i	$0.567223\pi$
$72$	−192.856	−0.315671
$73$	1231.66	1.97472	0.987359	−	0.158501i	$-0.0506660\pi$
$73$	1231.66	1.97472	0.987359	+	0.158501i	$0.0506660\pi$
$74$	1267.57	1.99124
$75$	−486.372	−0.748818
$76$	456.431	0.688898
$77$	0	0
$78$	2143.38	3.11141
$79$	−21.2513	−0.0302653	−0.0151326	−	0.999885i	$-0.504817\pi$
$79$	−21.2513	−0.0302653	−0.0151326	+	0.999885i	$0.504817\pi$
$80$	−424.644	−0.593458
$81$	−303.089	−0.415760
$82$	−1724.63	−2.32260
$83$	−400.284	−0.529360	−0.264680	−	0.964336i	$-0.585266\pi$
$83$	−400.284	−0.529360	−0.264680	+	0.964336i	$0.585266\pi$
$84$	0	0
$85$	217.424	0.277446
$86$	580.007	0.727254
$87$	811.695	1.00026
$88$	223.772	0.271070
$89$	298.970	0.356076	0.178038	−	0.984024i	$-0.443025\pi$
$89$	298.970	0.356076	0.178038	+	0.984024i	$0.443025\pi$
$90$	−1274.15	−1.49230
$91$	0	0
$92$	1936.70	2.19472
$93$	−470.308	−0.524394
$94$	−195.024	−0.213992
$95$	398.431	0.430297
$96$	2094.01	2.22624
$97$	218.811	0.229040	0.114520	−	0.993421i	$-0.463467\pi$
$97$	218.811	0.229040	0.114520	+	0.993421i	$0.463467\pi$
$98$	0	0
$99$	−1689.70	−1.71537
$100$	−555.403	−0.555403
$101$	−850.718	−0.838114	−0.419057	−	0.907960i	$-0.637639\pi$
$101$	−850.718	−0.838114	−0.419057	+	0.907960i	$0.637639\pi$
$102$	−905.065	−0.878577
$103$	−215.272	−0.205935	−0.102968	−	0.994685i	$-0.532834\pi$
$103$	−215.272	−0.205935	−0.102968	+	0.994685i	$0.532834\pi$
$104$	323.392	0.304915
$105$	0	0
$106$	−799.681	−0.732753
$107$	265.520	0.239895	0.119948	−	0.992780i	$-0.461727\pi$
$107$	265.520	0.239895	0.119948	+	0.992780i	$0.461727\pi$
$108$	830.476	0.739931
$109$	2136.73	1.87763	0.938817	−	0.344417i	$-0.111923\pi$
$109$	2136.73	1.87763	0.938817	+	0.344417i	$0.111923\pi$
$110$	1478.40	1.28146
$111$	−2465.89	−2.10858
$112$	0	0
$113$	2144.99	1.78570	0.892849	−	0.450356i	$-0.148703\pi$
$113$	2144.99	1.78570	0.892849	+	0.450356i	$0.148703\pi$
$114$	−1658.54	−1.36260
$115$	1690.59	1.37086
$116$	926.900	0.741901
$117$	−2441.93	−1.92954
$118$	−2819.85	−2.19990
$119$	0	0
$120$	−328.262	−0.249717
$121$	629.567	0.473003
$122$	2047.12	1.51916
$123$	3355.04	2.45946
$124$	−537.059	−0.388946
$125$	−1490.65	−1.06662
$126$	0	0
$127$	2164.27	1.51219	0.756093	−	0.654464i	$-0.227106\pi$
$127$	2164.27	1.51219	0.756093	+	0.654464i	$0.227106\pi$
$128$	639.385	0.441517
$129$	−1128.33	−0.770109
$130$	2136.57	1.44146
$131$	157.212	0.104852	0.0524261	−	0.998625i	$-0.483305\pi$
$131$	157.212	0.104852	0.0524261	+	0.998625i	$0.483305\pi$
$132$	−3294.72	−2.17249
$133$	0	0
$134$	−61.9586	−0.0399433
$135$	724.945	0.462173
$136$	−136.556	−0.0860998
$137$	2382.21	1.48559	0.742796	−	0.669518i	$-0.233499\pi$
$137$	2382.21	1.48559	0.742796	+	0.669518i	$0.233499\pi$
$138$	−7037.40	−4.34104
$139$	2763.52	1.68632	0.843162	−	0.537660i	$-0.180692\pi$
$139$	2763.52	1.68632	0.843162	+	0.537660i	$0.180692\pi$
$140$	0	0
$141$	379.395	0.226602
$142$	1040.75	0.615053
$143$	2833.38	1.65692
$144$	−2013.87	−1.16544
$145$	809.116	0.463403
$146$	−5110.69	−2.89701
$147$	0	0
$148$	−2815.88	−1.56394
$149$	−430.118	−0.236488	−0.118244	−	0.992985i	$-0.537726\pi$
$149$	−430.118	−0.236488	−0.118244	+	0.992985i	$0.537726\pi$
$150$	2018.17	1.09856
$151$	−1345.05	−0.724890	−0.362445	−	0.932005i	$-0.618058\pi$
$151$	−1345.05	−0.724890	−0.362445	+	0.932005i	$0.618058\pi$
$152$	−250.240	−0.133534
$153$	1031.13	0.544851
$154$	0	0
$155$	−468.814	−0.242942
$156$	−4761.48	−2.44374
$157$	2451.35	1.24611	0.623053	−	0.782180i	$-0.285892\pi$
$157$	2451.35	1.24611	0.623053	+	0.782180i	$0.285892\pi$
$158$	88.1812	0.0444008
$159$	1555.68	0.775932
$160$	2087.36	1.03138
$161$	0	0
$162$	1257.65	0.609942
$163$	178.699	0.0858697	0.0429348	−	0.999078i	$-0.486329\pi$
$163$	178.699	0.0858697	0.0429348	+	0.999078i	$0.486329\pi$
$164$	3831.23	1.82420
$165$	−2876.05	−1.35697
$166$	1660.96	0.776598
$167$	−1779.49	−0.824558	−0.412279	−	0.911058i	$-0.635267\pi$
$167$	−1779.49	−0.824558	−0.412279	+	0.911058i	$0.635267\pi$
$168$	0	0
$169$	1897.77	0.863800
$170$	−902.190	−0.407028
$171$	1889.56	0.845019
$172$	−1288.48	−0.571194
$173$	82.9688	0.0364624	0.0182312	−	0.999834i	$-0.494197\pi$
$173$	82.9688	0.0364624	0.0182312	+	0.999834i	$0.494197\pi$
$174$	−3368.09	−1.46744
$175$	0	0
$176$	2336.71	1.00077
$177$	5485.67	2.32954
$178$	−1240.56	−0.522382
$179$	3343.09	1.39595	0.697974	−	0.716124i	$-0.254085\pi$
$179$	3343.09	1.39595	0.697974	+	0.716124i	$0.254085\pi$
$180$	2830.51	1.17207
$181$	1394.41	0.572628	0.286314	−	0.958136i	$-0.407570\pi$
$181$	1394.41	0.572628	0.286314	+	0.958136i	$0.407570\pi$
$182$	0	0
$183$	−3982.42	−1.60868
$184$	−1061.80	−0.425418
$185$	−2458.06	−0.976864
$186$	1951.52	0.769313
$187$	−1196.43	−0.467869
$188$	433.243	0.168072
$189$	0	0
$190$	−1653.27	−0.631268
$191$	2393.54	0.906755	0.453378	−	0.891318i	$-0.350219\pi$
$191$	2393.54	0.906755	0.453378	+	0.891318i	$0.350219\pi$
$192$	−5281.03	−1.98503
$193$	−3179.52	−1.18584	−0.592920	−	0.805262i	$-0.702025\pi$
$193$	−3179.52	−1.18584	−0.592920	+	0.805262i	$0.702025\pi$
$194$	−907.944	−0.336013
$195$	−4156.42	−1.52640
$196$	0	0
$197$	1423.96	0.514990	0.257495	−	0.966280i	$-0.417103\pi$
$197$	1423.96	0.514990	0.257495	+	0.966280i	$0.417103\pi$
$198$	7011.33	2.51653
$199$	−2917.52	−1.03928	−0.519642	−	0.854384i	$-0.673935\pi$
$199$	−2917.52	−1.03928	−0.519642	+	0.854384i	$0.673935\pi$
$200$	304.501	0.107658
$201$	120.533	0.0422971
$202$	3530.01	1.22956
$203$	0	0
$204$	2010.59	0.690046
$205$	3344.38	1.13942
$206$	893.258	0.302118
$207$	8017.64	2.69210
$208$	3376.97	1.12573
$209$	−2192.47	−0.725627
$210$	0	0
$211$	5144.85	1.67861	0.839304	−	0.543662i	$-0.182963\pi$
$211$	5144.85	1.67861	0.839304	+	0.543662i	$0.182963\pi$
$212$	1776.48	0.575514
$213$	−2024.64	−0.651297
$214$	−1101.76	−0.351939
$215$	−1124.75	−0.356777
$216$	−455.311	−0.143426
$217$	0	0
$218$	−8866.27	−2.75459
$219$	9942.21	3.06773
$220$	−3284.25	−1.00647
$221$	−1729.06	−0.526286
$222$	10232.1	3.09339
$223$	1853.56	0.556607	0.278303	−	0.960493i	$-0.410228\pi$
$223$	1853.56	0.556607	0.278303	+	0.960493i	$0.410228\pi$
$224$	0	0
$225$	−2299.29	−0.681271
$226$	−8900.54	−2.61971
$227$	−3758.74	−1.09901	−0.549507	−	0.835489i	$-0.685185\pi$
$227$	−3758.74	−1.09901	−0.549507	+	0.835489i	$0.685185\pi$
$228$	3684.42	1.07020
$229$	−4808.91	−1.38769	−0.693847	−	0.720123i	$-0.744085\pi$
$229$	−4808.91	−1.38769	−0.693847	+	0.720123i	$0.744085\pi$
$230$	−7015.04	−2.01112
$231$	0	0
$232$	−508.176	−0.143808
$233$	−2975.58	−0.836638	−0.418319	−	0.908300i	$-0.637381\pi$
$233$	−2975.58	−0.836638	−0.418319	+	0.908300i	$0.637381\pi$
$234$	10132.7	2.83074
$235$	378.190	0.104980
$236$	6264.26	1.72783
$237$	−171.545	−0.0470172
$238$	0	0
$239$	5655.55	1.53066	0.765329	−	0.643639i	$-0.222576\pi$
$239$	5655.55	1.53066	0.765329	+	0.643639i	$0.222576\pi$
$240$	−3427.82	−0.921937
$241$	533.725	0.142657	0.0713284	−	0.997453i	$-0.477276\pi$
$241$	533.725	0.142657	0.0713284	+	0.997453i	$0.477276\pi$
$242$	−2612.36	−0.693921
$243$	−4879.13	−1.28805
$244$	−4547.65	−1.19317
$245$	0	0
$246$	−13921.6	−3.60816
$247$	−3168.52	−0.816227
$248$	294.444	0.0753921
$249$	−3231.18	−0.822361
$250$	6185.38	1.56479
$251$	−1346.92	−0.338714	−0.169357	−	0.985555i	$-0.554169\pi$
$251$	−1346.92	−0.338714	−0.169357	+	0.985555i	$0.554169\pi$
$252$	0	0
$253$	−9302.91	−2.31173
$254$	−8980.52	−2.21846
$255$	1755.10	0.431014
$256$	2580.68	0.630049
$257$	5676.23	1.37772	0.688860	−	0.724895i	$-0.258112\pi$
$257$	5676.23	1.37772	0.688860	+	0.724895i	$0.258112\pi$
$258$	4681.95	1.12979
$259$	0	0
$260$	−4746.35	−1.13214
$261$	3837.23	0.910033
$262$	−652.342	−0.153824
$263$	−3784.97	−0.887420	−0.443710	−	0.896171i	$-0.646338\pi$
$263$	−3784.97	−0.887420	−0.443710	+	0.896171i	$0.646338\pi$
$264$	1806.34	0.421108
$265$	1550.74	0.359475
$266$	0	0
$267$	2413.35	0.553164
$268$	137.640	0.0313720
$269$	−4266.18	−0.966966	−0.483483	−	0.875354i	$-0.660629\pi$
$269$	−4266.18	−0.966966	−0.483483	+	0.875354i	$0.660629\pi$
$270$	−3008.12	−0.678032
$271$	−118.952	−0.0266635	−0.0133318	−	0.999911i	$-0.504244\pi$
$271$	−118.952	−0.0266635	−0.0133318	+	0.999911i	$0.504244\pi$
$272$	−1425.97	−0.317874
$273$	0	0
$274$	−9884.87	−2.17944
$275$	2667.88	0.585014
$276$	15633.5	3.40951
$277$	−213.872	−0.0463910	−0.0231955	−	0.999731i	$-0.507384\pi$
$277$	−213.872	−0.0463910	−0.0231955	+	0.999731i	$0.507384\pi$
$278$	−11467.1	−2.47392
$279$	−2223.35	−0.477091
$280$	0	0
$281$	1202.18	0.255217	0.127608	−	0.991825i	$-0.459270\pi$
$281$	1202.18	0.255217	0.127608	+	0.991825i	$0.459270\pi$
$282$	−1574.28	−0.332436
$283$	2626.11	0.551612	0.275806	−	0.961213i	$-0.411055\pi$
$283$	2626.11	0.551612	0.275806	+	0.961213i	$0.411055\pi$
$284$	−2312.00	−0.483071
$285$	3216.23	0.668467
$286$	−11757.0	−2.43079
$287$	0	0
$288$	9899.31	2.02543
$289$	−4182.88	−0.851391
$290$	−3357.39	−0.679836
$291$	1766.29	0.355814
$292$	11353.3	2.27535
$293$	−2393.25	−0.477185	−0.238592	−	0.971120i	$-0.576686\pi$
$293$	−2393.25	−0.477185	−0.238592	+	0.971120i	$0.576686\pi$
$294$	0	0
$295$	5468.24	1.07923
$296$	1543.81	0.303150
$297$	−3989.19	−0.779381
$298$	1784.75	0.346939
$299$	−13444.4	−2.60037
$300$	−4483.34	−0.862820
$301$	0	0
$302$	5581.21	1.06345
$303$	−6867.19	−1.30201
$304$	−2613.09	−0.492997
$305$	−3969.77	−0.745273
$306$	−4278.63	−0.799324
$307$	5361.68	0.996766	0.498383	−	0.866957i	$-0.333927\pi$
$307$	5361.68	0.996766	0.498383	+	0.866957i	$0.333927\pi$
$308$	0	0
$309$	−1737.72	−0.319921
$310$	1945.32	0.356409
$311$	3993.76	0.728184	0.364092	−	0.931363i	$-0.381379\pi$
$311$	3993.76	0.728184	0.364092	+	0.931363i	$0.381379\pi$
$312$	2610.50	0.473687
$313$	−9169.19	−1.65583	−0.827913	−	0.560857i	$-0.810472\pi$
$313$	−9169.19	−1.65583	−0.827913	+	0.560857i	$0.810472\pi$
$314$	−10171.7	−1.82810
$315$	0	0
$316$	−195.893	−0.0348729
$317$	−332.285	−0.0588737	−0.0294368	−	0.999567i	$-0.509371\pi$
$317$	−332.285	−0.0588737	−0.0294368	+	0.999567i	$0.509371\pi$
$318$	−6455.21	−1.13833
$319$	−4452.36	−0.781455
$320$	−5264.26	−0.919628
$321$	2143.34	0.372677
$322$	0	0
$323$	1337.94	0.230480
$324$	−2793.86	−0.479056
$325$	3855.58	0.658058
$326$	−741.501	−0.125975
$327$	17248.2	2.91691
$328$	−2100.48	−0.353597
$329$	0	0
$330$	11934.0	1.99075
$331$	−5471.22	−0.908537	−0.454268	−	0.890865i	$-0.650099\pi$
$331$	−5471.22	−0.908537	−0.454268	+	0.890865i	$0.650099\pi$
$332$	−3689.79	−0.609951
$333$	−11657.3	−1.91837
$334$	7383.91	1.20967
$335$	120.150	0.0195955
$336$	0	0
$337$	−29.3024	−0.00473651	−0.00236826	−	0.999997i	$-0.500754\pi$
$337$	−29.3024	−0.00473651	−0.00236826	+	0.999997i	$0.500754\pi$
$338$	−7874.69	−1.26724
$339$	17314.9	2.77409
$340$	2004.20	0.319685
$341$	2579.76	0.409683
$342$	−7840.63	−1.23969
$343$	0	0
$344$	706.411	0.110718
$345$	13646.9	2.12963
$346$	−344.275	−0.0534923
$347$	7566.21	1.17053	0.585267	−	0.810841i	$-0.300990\pi$
$347$	7566.21	1.17053	0.585267	+	0.810841i	$0.300990\pi$
$348$	7482.15	1.15254
$349$	−1384.20	−0.212306	−0.106153	−	0.994350i	$-0.533853\pi$
$349$	−1384.20	−0.212306	−0.106153	+	0.994350i	$0.533853\pi$
$350$	0	0
$351$	−5765.12	−0.876693
$352$	−11486.2	−1.73925
$353$	4418.01	0.666139	0.333069	−	0.942902i	$-0.391916\pi$
$353$	4418.01	0.666139	0.333069	+	0.942902i	$0.391916\pi$
$354$	−22762.5	−3.41755
$355$	−2018.21	−0.301734
$356$	2755.89	0.410285
$357$	0	0
$358$	−13872.0	−2.04793
$359$	7290.24	1.07177	0.535883	−	0.844292i	$-0.319979\pi$
$359$	7290.24	1.07177	0.535883	+	0.844292i	$0.319979\pi$
$360$	−1551.83	−0.227191
$361$	−4407.21	−0.642544
$362$	−5786.03	−0.840075
$363$	5082.01	0.734811
$364$	0	0
$365$	9910.62	1.42122
$366$	16524.9	2.36002
$367$	−3083.64	−0.438596	−0.219298	−	0.975658i	$-0.570377\pi$
$367$	−3083.64	−0.438596	−0.219298	+	0.975658i	$0.570377\pi$
$368$	−11087.7	−1.57061
$369$	15860.7	2.23760
$370$	10199.6	1.43311
$371$	0	0
$372$	−4335.27	−0.604229
$373$	−698.429	−0.0969525	−0.0484763	−	0.998824i	$-0.515437\pi$
$373$	−698.429	−0.0969525	−0.0484763	+	0.998824i	$0.515437\pi$
$374$	4964.52	0.686388
$375$	−12032.9	−1.65700
$376$	−237.527	−0.0325785
$377$	−6434.48	−0.879026
$378$	0	0
$379$	7422.49	1.00598	0.502991	−	0.864291i	$-0.332233\pi$
$379$	7422.49	1.00598	0.502991	+	0.864291i	$0.332233\pi$
$380$	3672.72	0.495806
$381$	17470.5	2.34918
$382$	−9931.86	−1.33026
$383$	1033.32	0.137860	0.0689301	−	0.997621i	$-0.478041\pi$
$383$	1033.32	0.137860	0.0689301	+	0.997621i	$0.478041\pi$
$384$	5161.26	0.685897
$385$	0	0
$386$	13193.3	1.73969
$387$	−5334.11	−0.700641
$388$	2016.98	0.263909
$389$	8427.69	1.09846	0.549230	−	0.835671i	$-0.314921\pi$
$389$	8427.69	1.09846	0.549230	+	0.835671i	$0.314921\pi$
$390$	17246.9	2.23931
$391$	5677.06	0.734275
$392$	0	0
$393$	1269.05	0.162888
$394$	−5908.66	−0.755518
$395$	−171.000	−0.0217822
$396$	−15575.5	−1.97652
$397$	11124.8	1.40640	0.703199	−	0.710993i	$-0.251754\pi$
$397$	11124.8	1.40640	0.703199	+	0.710993i	$0.251754\pi$
$398$	12106.1	1.52468
$399$	0	0
$400$	3179.71	0.397464
$401$	−9360.64	−1.16571	−0.582853	−	0.812578i	$-0.698064\pi$
$401$	−9360.64	−1.16571	−0.582853	+	0.812578i	$0.698064\pi$
$402$	−500.144	−0.0620520
$403$	3728.23	0.460835
$404$	−7841.86	−0.965711
$405$	−2438.83	−0.299226
$406$	0	0
$407$	13526.0	1.64732
$408$	−1102.31	−0.133756
$409$	10154.2	1.22761	0.613806	−	0.789457i	$-0.289638\pi$
$409$	10154.2	1.22761	0.613806	+	0.789457i	$0.289638\pi$
$410$	−13877.3	−1.67159
$411$	19229.8	2.30787
$412$	−1984.36	−0.237287
$413$	0	0
$414$	−33268.8	−3.94945
$415$	−3220.92	−0.380985
$416$	−16599.7	−1.95641
$417$	22307.8	2.61971
$418$	9097.53	1.06453
$419$	6249.51	0.728660	0.364330	−	0.931270i	$-0.381298\pi$
$419$	6249.51	0.728660	0.364330	+	0.931270i	$0.381298\pi$
$420$	0	0
$421$	43.3154	0.00501440	0.00250720	−	0.999997i	$-0.499202\pi$
$421$	43.3154	0.00501440	0.00250720	+	0.999997i	$0.499202\pi$
$422$	−21348.3	−2.46261
$423$	1793.56	0.206161
$424$	−973.959	−0.111556
$425$	−1628.06	−0.185818
$426$	8401.15	0.955486
$427$	0	0
$428$	2447.55	0.276417
$429$	22871.7	2.57403
$430$	4667.08	0.523411
$431$	10561.6	1.18035	0.590177	−	0.807274i	$-0.299058\pi$
$431$	10561.6	1.18035	0.590177	+	0.807274i	$0.299058\pi$
$432$	−4754.52	−0.529518
$433$	−11761.4	−1.30535	−0.652676	−	0.757637i	$-0.726354\pi$
$433$	−11761.4	−1.30535	−0.652676	+	0.757637i	$0.726354\pi$
$434$	0	0
$435$	6531.37	0.719897
$436$	19696.3	2.16349
$437$	10403.3	1.13880
$438$	−41254.7	−4.50052
$439$	−9095.22	−0.988818	−0.494409	−	0.869229i	$-0.664615\pi$
$439$	−9095.22	−0.988818	−0.494409	+	0.869229i	$0.664615\pi$
$440$	1800.60	0.195091
$441$	0	0
$442$	7174.66	0.772089
$443$	−4751.69	−0.509615	−0.254808	−	0.966992i	$-0.582012\pi$
$443$	−4751.69	−0.509615	−0.254808	+	0.966992i	$0.582012\pi$
$444$	−22730.4	−2.42959
$445$	2405.69	0.256271
$446$	−7691.24	−0.816571
$447$	−3472.01	−0.367384
$448$	0	0
$449$	−14806.2	−1.55624	−0.778118	−	0.628118i	$-0.783826\pi$
$449$	−14806.2	−1.55624	−0.778118	+	0.628118i	$0.783826\pi$
$450$	9540.78	0.999460
$451$	−18403.3	−1.92146
$452$	19772.4	2.05756
$453$	−10857.5	−1.12612
$454$	15596.7	1.61231
$455$	0	0
$456$	−2019.99	−0.207445
$457$	−644.024	−0.0659216	−0.0329608	−	0.999457i	$-0.510494\pi$
$457$	−644.024	−0.0659216	−0.0329608	+	0.999457i	$0.510494\pi$
$458$	19954.3	2.03582
$459$	2434.39	0.247554
$460$	15583.8	1.57956
$461$	17403.9	1.75831	0.879155	−	0.476536i	$-0.158108\pi$
$461$	17403.9	1.75831	0.879155	+	0.476536i	$0.158108\pi$
$462$	0	0
$463$	−7283.63	−0.731099	−0.365550	−	0.930792i	$-0.619119\pi$
$463$	−7283.63	−0.731099	−0.365550	+	0.930792i	$0.619119\pi$
$464$	−5306.55	−0.530927
$465$	−3784.37	−0.377411
$466$	12347.0	1.22739
$467$	−1665.02	−0.164985	−0.0824926	−	0.996592i	$-0.526288\pi$
$467$	−1665.02	−0.164985	−0.0824926	+	0.996592i	$0.526288\pi$
$468$	−22509.6	−2.22330
$469$	0	0
$470$	−1569.28	−0.154012
$471$	19787.8	1.93583
$472$	−3434.40	−0.334917
$473$	6189.19	0.601648
$474$	711.819	0.0689766
$475$	−2983.43	−0.288188
$476$	0	0
$477$	7354.36	0.705939
$478$	−23467.4	−2.24556
$479$	−1819.98	−0.173606	−0.0868029	−	0.996226i	$-0.527665\pi$
$479$	−1819.98	−0.173606	−0.0868029	+	0.996226i	$0.527665\pi$
$480$	16849.7	1.60225
$481$	19547.7	1.85301
$482$	−2214.67	−0.209285
$483$	0	0
$484$	5803.31	0.545014
$485$	1760.68	0.164842
$486$	20245.7	1.88964
$487$	−10813.6	−1.00618	−0.503090	−	0.864234i	$-0.667804\pi$
$487$	−10813.6	−1.00618	−0.503090	+	0.864234i	$0.667804\pi$
$488$	2493.26	0.231280
$489$	1442.50	0.133399
$490$	0	0
$491$	−16588.0	−1.52466	−0.762330	−	0.647189i	$-0.775945\pi$
$491$	−16588.0	−1.52466	−0.762330	+	0.647189i	$0.775945\pi$
$492$	30926.5	2.83389
$493$	2717.03	0.248213
$494$	13147.6	1.19745
$495$	−13596.3	−1.23456
$496$	3074.69	0.278342
$497$	0	0
$498$	13407.6	1.20645
$499$	8716.25	0.781949	0.390975	−	0.920401i	$-0.372138\pi$
$499$	8716.25	0.781949	0.390975	+	0.920401i	$0.372138\pi$
$500$	−13740.7	−1.22901
$501$	−14364.5	−1.28095
$502$	5589.00	0.496911
$503$	13703.8	1.21476	0.607379	−	0.794412i	$-0.292221\pi$
$503$	13703.8	1.21476	0.607379	+	0.794412i	$0.292221\pi$
$504$	0	0
$505$	−6845.37	−0.603198
$506$	38602.0	3.39144
$507$	15319.2	1.34191
$508$	19950.1	1.74240
$509$	16381.7	1.42653	0.713265	−	0.700894i	$-0.247215\pi$
$509$	16381.7	1.42653	0.713265	+	0.700894i	$0.247215\pi$
$510$	−7282.69	−0.632319
$511$	0	0
$512$	−15823.5	−1.36583
$513$	4461.03	0.383936
$514$	−23553.3	−2.02119
$515$	−1732.20	−0.148213
$516$	−10400.9	−0.887352
$517$	−2081.08	−0.177032
$518$	0	0
$519$	669.743	0.0566444
$520$	2602.20	0.219450
$521$	−20900.7	−1.75753	−0.878767	−	0.477251i	$-0.841633\pi$
$521$	−20900.7	−1.75753	−0.878767	+	0.477251i	$0.841633\pi$
$522$	−15922.4	−1.33507
$523$	−3337.04	−0.279003	−0.139501	−	0.990222i	$-0.544550\pi$
$523$	−3337.04	−0.279003	−0.139501	+	0.990222i	$0.544550\pi$
$524$	1449.17	0.120815
$525$	0	0
$526$	15705.6	1.30189
$527$	−1574.29	−0.130127
$528$	18862.4	1.55470
$529$	31975.4	2.62804
$530$	−6434.70	−0.527369
$531$	25933.1	2.11940
$532$	0	0
$533$	−26596.2	−2.16136
$534$	−10014.1	−0.811521
$535$	2136.53	0.172655
$536$	−75.4615	−0.00608105
$537$	26986.2	2.16861
$538$	17702.3	1.41859
$539$	0	0
$540$	6682.50	0.532535
$541$	8834.77	0.702101	0.351050	−	0.936357i	$-0.385825\pi$
$541$	8834.77	0.702101	0.351050	+	0.936357i	$0.385825\pi$
$542$	493.586	0.0391168
$543$	11256.0	0.889579
$544$	7009.42	0.552438
$545$	17193.4	1.35135
$546$	0	0
$547$	6886.71	0.538308	0.269154	−	0.963097i	$-0.413256\pi$
$547$	6886.71	0.538308	0.269154	+	0.963097i	$0.413256\pi$
$548$	21959.1	1.71176
$549$	−18826.6	−1.46357
$550$	−11070.2	−0.858247
$551$	4978.99	0.384958
$552$	−8571.09	−0.660888
$553$	0	0
$554$	887.451	0.0680581
$555$	−19842.0	−1.51756
$556$	25474.0	1.94305
$557$	143.666	0.0109288	0.00546438	−	0.999985i	$-0.498261\pi$
$557$	143.666	0.0109288	0.00546438	+	0.999985i	$0.498261\pi$
$558$	9225.67	0.699917
$559$	8944.53	0.676768
$560$	0	0
$561$	−9657.85	−0.726835
$562$	−4988.38	−0.374416
$563$	−19242.7	−1.44047	−0.720233	−	0.693732i	$-0.755965\pi$
$563$	−19242.7	−1.44047	−0.720233	+	0.693732i	$0.755965\pi$
$564$	3497.24	0.261100
$565$	17259.9	1.28518
$566$	−10896.9	−0.809244
$567$	0	0
$568$	1267.56	0.0936369
$569$	11458.7	0.844243	0.422121	−	0.906539i	$-0.361286\pi$
$569$	11458.7	0.844243	0.422121	+	0.906539i	$0.361286\pi$
$570$	−13345.6	−0.980676
$571$	4168.59	0.305516	0.152758	−	0.988264i	$-0.451184\pi$
$571$	4168.59	0.305516	0.152758	+	0.988264i	$0.451184\pi$
$572$	26118.0	1.90917
$573$	19321.2	1.40865
$574$	0	0
$575$	−12659.1	−0.918123
$576$	−24965.7	−1.80597
$577$	−9207.00	−0.664285	−0.332143	−	0.943229i	$-0.607772\pi$
$577$	−9207.00	−0.664285	−0.332143	+	0.943229i	$0.607772\pi$
$578$	17356.7	1.24904
$579$	−25665.8	−1.84220
$580$	7458.38	0.533952
$581$	0	0
$582$	−7329.13	−0.521997
$583$	−8533.30	−0.606197
$584$	−6224.49	−0.441047
$585$	−19649.2	−1.38871
$586$	9930.67	0.700055
$587$	−12692.9	−0.892494	−0.446247	−	0.894910i	$-0.647240\pi$
$587$	−12692.9	−0.892494	−0.446247	+	0.894910i	$0.647240\pi$
$588$	0	0
$589$	−2884.90	−0.201817
$590$	−22690.2	−1.58329
$591$	11494.6	0.800039
$592$	16121.0	1.11921
$593$	4349.31	0.301188	0.150594	−	0.988596i	$-0.451881\pi$
$593$	4349.31	0.301188	0.150594	+	0.988596i	$0.451881\pi$
$594$	16552.9	1.14339
$595$	0	0
$596$	−3964.80	−0.272491
$597$	−23550.9	−1.61453
$598$	55787.0	3.81488
$599$	25898.6	1.76659	0.883295	−	0.468818i	$-0.155320\pi$
$599$	25898.6	1.76659	0.883295	+	0.468818i	$0.155320\pi$
$600$	2458.01	0.167246
$601$	18497.5	1.25545	0.627727	−	0.778433i	$-0.283985\pi$
$601$	18497.5	1.25545	0.627727	+	0.778433i	$0.283985\pi$
$602$	0	0
$603$	569.809	0.0384816
$604$	−12398.6	−0.835249
$605$	5065.87	0.340425
$606$	28495.1	1.91012
$607$	−1322.90	−0.0884592	−0.0442296	−	0.999021i	$-0.514083\pi$
$607$	−1322.90	−0.0884592	−0.0442296	+	0.999021i	$0.514083\pi$
$608$	12844.8	0.856787
$609$	0	0
$610$	16472.4	1.09335
$611$	−3007.55	−0.199136
$612$	9504.92	0.627800
$613$	24437.9	1.61018	0.805088	−	0.593155i	$-0.202118\pi$
$613$	24437.9	1.61018	0.805088	+	0.593155i	$0.202118\pi$
$614$	−22248.0	−1.46231
$615$	26996.6	1.77010
$616$	0	0
$617$	−25717.9	−1.67806	−0.839029	−	0.544086i	$-0.816876\pi$
$617$	−25717.9	−1.67806	−0.839029	+	0.544086i	$0.816876\pi$
$618$	7210.59	0.469340
$619$	12658.7	0.821965	0.410983	−	0.911643i	$-0.365186\pi$
$619$	12658.7	0.821965	0.410983	+	0.911643i	$0.365186\pi$
$620$	−4321.49	−0.279928
$621$	18928.7	1.22316
$622$	−16571.9	−1.06828
$623$	0	0
$624$	27259.7	1.74882
$625$	−4463.09	−0.285638
$626$	38047.1	2.42918
$627$	−17698.1	−1.12726
$628$	22596.3	1.43582
$629$	−8254.22	−0.523239
$630$	0	0
$631$	13863.9	0.874663	0.437332	−	0.899300i	$-0.355924\pi$
$631$	13863.9	0.874663	0.437332	+	0.899300i	$0.355924\pi$
$632$	107.399	0.00675966
$633$	41530.4	2.60772
$634$	1378.80	0.0863708
$635$	17415.0	1.08833
$636$	14340.1	0.894062
$637$	0	0
$638$	18474.8	1.14644
$639$	−9571.36	−0.592546
$640$	5144.87	0.317764
$641$	7948.21	0.489759	0.244879	−	0.969554i	$-0.421252\pi$
$641$	7948.21	0.489759	0.244879	+	0.969554i	$0.421252\pi$
$642$	−8893.67	−0.546737
$643$	25277.9	1.55033	0.775167	−	0.631756i	$-0.217666\pi$
$643$	25277.9	1.55033	0.775167	+	0.631756i	$0.217666\pi$
$644$	0	0
$645$	−9079.21	−0.554254
$646$	−5551.73	−0.338127
$647$	7944.04	0.482708	0.241354	−	0.970437i	$-0.422408\pi$
$647$	7944.04	0.482708	0.241354	+	0.970437i	$0.422408\pi$
$648$	1531.74	0.0928587
$649$	−30090.3	−1.81995
$650$	−15998.5	−0.965406
$651$	0	0
$652$	1647.23	0.0989426
$653$	−5912.12	−0.354302	−0.177151	−	0.984184i	$-0.556688\pi$
$653$	−5912.12	−0.354302	−0.177151	+	0.984184i	$0.556688\pi$
$654$	−71570.6	−4.27925
$655$	1265.02	0.0754631
$656$	−21934.0	−1.30545
$657$	47001.1	2.79100
$658$	0	0
$659$	−7844.69	−0.463711	−0.231856	−	0.972750i	$-0.574480\pi$
$659$	−7844.69	−0.463711	−0.231856	+	0.972750i	$0.574480\pi$
$660$	−26511.2	−1.56356
$661$	−15408.0	−0.906660	−0.453330	−	0.891343i	$-0.649764\pi$
$661$	−15408.0	−0.906660	−0.453330	+	0.891343i	$0.649764\pi$
$662$	22702.6	1.33287
$663$	−13957.4	−0.817587
$664$	2022.94	0.118231
$665$	0	0
$666$	48371.5	2.81435
$667$	21126.5	1.22642
$668$	−16403.2	−0.950090
$669$	14962.3	0.864690
$670$	−498.555	−0.0287476
$671$	21844.6	1.25678
$672$	0	0
$673$	−31599.0	−1.80988	−0.904941	−	0.425537i	$-0.860085\pi$
$673$	−31599.0	−1.80988	−0.904941	+	0.425537i	$0.860085\pi$
$674$	121.589	0.00694871
$675$	−5428.35	−0.309537
$676$	17493.5	0.995306
$677$	−12259.8	−0.695984	−0.347992	−	0.937498i	$-0.613136\pi$
$677$	−12259.8	−0.695984	−0.347992	+	0.937498i	$0.613136\pi$
$678$	−71847.2	−4.06973
$679$	0	0
$680$	−1098.81	−0.0619668
$681$	−30341.4	−1.70732
$682$	−10704.6	−0.601026
$683$	30165.2	1.68995	0.844977	−	0.534802i	$-0.179614\pi$
$683$	30165.2	1.68995	0.844977	+	0.534802i	$0.179614\pi$
$684$	17417.8	0.973666
$685$	19168.7	1.06919
$686$	0	0
$687$	−38818.6	−2.15578
$688$	7376.60	0.408765
$689$	−12332.2	−0.681886
$690$	−56627.0	−3.12428
$691$	−12858.0	−0.707873	−0.353937	−	0.935269i	$-0.615157\pi$
$691$	−12858.0	−0.707873	−0.353937	+	0.935269i	$0.615157\pi$
$692$	764.801	0.0420135
$693$	0	0
$694$	−31395.6	−1.71723
$695$	22236.9	1.21366
$696$	−4102.11	−0.223405
$697$	11230.5	0.610311
$698$	5743.68	0.311463
$699$	−24019.6	−1.29972
$700$	0	0
$701$	18285.6	0.985220	0.492610	−	0.870250i	$-0.336043\pi$
$701$	18285.6	0.985220	0.492610	+	0.870250i	$0.336043\pi$
$702$	23922.1	1.28615
$703$	−15125.9	−0.811501
$704$	28967.8	1.55080
$705$	3052.83	0.163087
$706$	−18332.3	−0.977260
$707$	0	0
$708$	50566.5	2.68419
$709$	−9061.05	−0.479964	−0.239982	−	0.970777i	$-0.577142\pi$
$709$	−9061.05	−0.479964	−0.239982	+	0.970777i	$0.577142\pi$
$710$	8374.46	0.442659
$711$	−810.969	−0.0427760
$712$	−1510.92	−0.0795284
$713$	−12241.0	−0.642957
$714$	0	0
$715$	22799.1	1.19250
$716$	30816.4	1.60847
$717$	45652.9	2.37788
$718$	−30250.5	−1.57234
$719$	−19624.4	−1.01789	−0.508946	−	0.860798i	$-0.669965\pi$
$719$	−19624.4	−1.01789	−0.508946	+	0.860798i	$0.669965\pi$
$720$	−16204.8	−0.838774
$721$	0	0
$722$	18287.5	0.942645
$723$	4308.35	0.221617
$724$	12853.6	0.659806
$725$	−6058.62	−0.310361
$726$	−21087.6	−1.07801
$727$	−16926.2	−0.863490	−0.431745	−	0.901996i	$-0.642102\pi$
$727$	−16926.2	−0.863490	−0.431745	+	0.901996i	$0.642102\pi$
$728$	0	0
$729$	−31202.1	−1.58523
$730$	−41123.6	−2.08501
$731$	−3776.93	−0.191101
$732$	−36709.7	−1.85359
$733$	20290.1	1.02242	0.511208	−	0.859457i	$-0.329198\pi$
$733$	20290.1	1.02242	0.511208	+	0.859457i	$0.329198\pi$
$734$	12795.4	0.643443
$735$	0	0
$736$	54502.2	2.72959
$737$	−661.153	−0.0330446
$738$	−65813.3	−3.28268
$739$	−28103.3	−1.39891	−0.699457	−	0.714675i	$-0.746575\pi$
$739$	−28103.3	−1.39891	−0.699457	+	0.714675i	$0.746575\pi$
$740$	−22658.2	−1.12558
$741$	−25577.0	−1.26801
$742$	0	0
$743$	−10015.9	−0.494548	−0.247274	−	0.968946i	$-0.579535\pi$
$743$	−10015.9	−0.494548	−0.247274	+	0.968946i	$0.579535\pi$
$744$	2376.82	0.117122
$745$	−3460.98	−0.170202
$746$	2898.10	0.142234
$747$	−15275.2	−0.748180
$748$	−11028.6	−0.539098
$749$	0	0
$750$	49929.8	2.43090
$751$	−9322.29	−0.452963	−0.226481	−	0.974015i	$-0.572722\pi$
$751$	−9322.29	−0.452963	−0.226481	+	0.974015i	$0.572722\pi$
$752$	−2480.34	−0.120277
$753$	−10872.7	−0.526192
$754$	26699.6	1.28958
$755$	−10823.0	−0.521710
$756$	0	0
$757$	38972.2	1.87116	0.935580	−	0.353116i	$-0.114878\pi$
$757$	38972.2	1.87116	0.935580	+	0.353116i	$0.114878\pi$
$758$	−30799.2	−1.47583
$759$	−75095.2	−3.59128
$760$	−2013.58	−0.0961054
$761$	27652.9	1.31723	0.658617	−	0.752478i	$-0.271142\pi$
$761$	27652.9	1.31723	0.658617	+	0.752478i	$0.271142\pi$
$762$	−72492.8	−3.44638
$763$	0	0
$764$	22063.5	1.04480
$765$	8297.10	0.392134
$766$	−4287.73	−0.202248
$767$	−43486.1	−2.04719
$768$	20831.9	0.978782
$769$	17391.4	0.815540	0.407770	−	0.913085i	$-0.366306\pi$
$769$	17391.4	0.815540	0.407770	+	0.913085i	$0.366306\pi$
$770$	0	0
$771$	45819.9	2.14029
$772$	−29308.6	−1.36637
$773$	29820.8	1.38755	0.693776	−	0.720190i	$-0.255946\pi$
$773$	29820.8	1.38755	0.693776	+	0.720190i	$0.255946\pi$
$774$	22133.6	1.02788
$775$	3510.45	0.162709
$776$	−1105.82	−0.0511553
$777$	0	0
$778$	−34970.3	−1.61150
$779$	20580.0	0.946542
$780$	−38313.7	−1.75878
$781$	11105.7	0.508826
$782$	−23556.7	−1.07722
$783$	9059.26	0.413476
$784$	0	0
$785$	19725.0	0.896833
$786$	−5265.85	−0.238965
$787$	20425.7	0.925155	0.462578	−	0.886579i	$-0.346925\pi$
$787$	20425.7	0.925155	0.462578	+	0.886579i	$0.346925\pi$
$788$	13126.0	0.593394
$789$	−30553.2	−1.37861
$790$	709.558	0.0319556
$791$	0	0
$792$	8539.34	0.383122
$793$	31569.5	1.41370
$794$	−46162.0	−2.06326
$795$	12517.9	0.558445
$796$	−26893.5	−1.19751
$797$	−15796.2	−0.702047	−0.351023	−	0.936367i	$-0.614166\pi$
$797$	−15796.2	−0.702047	−0.351023	+	0.936367i	$0.614166\pi$
$798$	0	0
$799$	1269.97	0.0562307
$800$	−15630.1	−0.690758
$801$	11409.0	0.503266
$802$	38841.5	1.71015
$803$	−54535.6	−2.39666
$804$	1111.06	0.0487365
$805$	0	0
$806$	−15470.1	−0.676069
$807$	−34437.6	−1.50218
$808$	4299.32	0.187190
$809$	14447.5	0.627871	0.313936	−	0.949444i	$-0.398352\pi$
$809$	14447.5	0.627871	0.313936	+	0.949444i	$0.398352\pi$
$810$	10119.8	0.438980
$811$	−18015.7	−0.780045	−0.390023	−	0.920805i	$-0.627533\pi$
$811$	−18015.7	−0.780045	−0.390023	+	0.920805i	$0.627533\pi$
$812$	0	0
$813$	−960.208	−0.0414219
$814$	−56125.6	−2.41671
$815$	1437.91	0.0618011
$816$	−11510.7	−0.493818
$817$	−6921.26	−0.296382
$818$	−42134.4	−1.80097
$819$	0	0
$820$	30828.3	1.31289
$821$	−26929.8	−1.14477	−0.572385	−	0.819985i	$-0.693982\pi$
$821$	−26929.8	−1.14477	−0.572385	+	0.819985i	$0.693982\pi$
$822$	−79792.9	−3.38576
$823$	−21242.8	−0.899731	−0.449866	−	0.893096i	$-0.648528\pi$
$823$	−21242.8	−0.899731	−0.449866	+	0.893096i	$0.648528\pi$
$824$	1087.93	0.0459950
$825$	21535.7	0.908821
$826$	0	0
$827$	−3792.28	−0.159457	−0.0797283	−	0.996817i	$-0.525405\pi$
$827$	−3792.28	−0.159457	−0.0797283	+	0.996817i	$0.525405\pi$
$828$	73906.1	3.10195
$829$	−18415.1	−0.771512	−0.385756	−	0.922601i	$-0.626059\pi$
$829$	−18415.1	−0.771512	−0.385756	+	0.922601i	$0.626059\pi$
$830$	13365.0	0.558925
$831$	−1726.42	−0.0720686
$832$	41863.9	1.74444
$833$	0	0
$834$	−92565.1	−3.84325
$835$	−14318.8	−0.593441
$836$	−20210.0	−0.836098
$837$	−5249.07	−0.216767
$838$	−25932.0	−1.06898
$839$	−33307.5	−1.37057	−0.685283	−	0.728277i	$-0.740321\pi$
$839$	−33307.5	−1.37057	−0.685283	+	0.728277i	$0.740321\pi$
$840$	0	0
$841$	−14277.9	−0.585424
$842$	−179.735	−0.00735639
$843$	9704.26	0.396480
$844$	47424.9	1.93416
$845$	15270.6	0.621684
$846$	−7442.30	−0.302449
$847$	0	0
$848$	−10170.4	−0.411856
$849$	21198.6	0.856930
$850$	6755.56	0.272604
$851$	−64181.2	−2.58531
$852$	−18663.0	−0.750451
$853$	17643.6	0.708213	0.354107	−	0.935205i	$-0.384785\pi$
$853$	17643.6	0.708213	0.354107	+	0.935205i	$0.384785\pi$
$854$	0	0
$855$	15204.5	0.608168
$856$	−1341.87	−0.0535798
$857$	−27292.5	−1.08786	−0.543928	−	0.839132i	$-0.683064\pi$
$857$	−27292.5	−1.08786	−0.543928	+	0.839132i	$0.683064\pi$
$858$	−94905.1	−3.77623
$859$	−28096.9	−1.11601	−0.558005	−	0.829838i	$-0.688433\pi$
$859$	−28096.9	−1.11601	−0.558005	+	0.829838i	$0.688433\pi$
$860$	−10367.8	−0.411094
$861$	0	0
$862$	−43824.7	−1.73164
$863$	−11638.4	−0.459067	−0.229534	−	0.973301i	$-0.573720\pi$
$863$	−11638.4	−0.459067	−0.229534	+	0.973301i	$0.573720\pi$
$864$	23371.1	0.920257
$865$	667.616	0.0262423
$866$	48803.4	1.91502
$867$	−33765.2	−1.32264
$868$	0	0
$869$	940.971	0.0367322
$870$	−27101.6	−1.05613
$871$	−955.488	−0.0371705
$872$	−10798.5	−0.419363
$873$	8350.01	0.323717
$874$	−43167.8	−1.67068
$875$	0	0
$876$	91646.6	3.53476
$877$	−33177.9	−1.27747	−0.638733	−	0.769428i	$-0.720541\pi$
$877$	−33177.9	−1.27747	−0.638733	+	0.769428i	$0.720541\pi$
$878$	37740.2	1.45065
$879$	−19318.9	−0.741307
$880$	18802.5	0.720264
$881$	43170.3	1.65090	0.825452	−	0.564473i	$-0.190920\pi$
$881$	43170.3	1.65090	0.825452	+	0.564473i	$0.190920\pi$
$882$	0	0
$883$	−3337.29	−0.127190	−0.0635949	−	0.997976i	$-0.520257\pi$
$883$	−3337.29	−0.127190	−0.0635949	+	0.997976i	$0.520257\pi$
$884$	−15938.4	−0.606409
$885$	44140.9	1.67659
$886$	19716.9	0.747632
$887$	6107.32	0.231188	0.115594	−	0.993297i	$-0.463123\pi$
$887$	6107.32	0.231188	0.115594	+	0.993297i	$0.463123\pi$
$888$	12462.0	0.470943
$889$	0	0
$890$	−9982.28	−0.375963
$891$	13420.3	0.504597
$892$	17086.0	0.641346
$893$	2327.23	0.0872093
$894$	14406.9	0.538971
$895$	26900.5	1.00468
$896$	0	0
$897$	−108527.	−4.03968
$898$	61437.8	2.28308
$899$	−5858.52	−0.217344
$900$	−21194.7	−0.784989
$901$	5207.41	0.192546
$902$	76363.5	2.81887
$903$	0	0
$904$	−10840.3	−0.398830
$905$	11220.2	0.412125
$906$	45052.8	1.65207
$907$	47378.3	1.73448	0.867238	−	0.497893i	$-0.165893\pi$
$907$	47378.3	1.73448	0.867238	+	0.497893i	$0.165893\pi$
$908$	−34647.8	−1.26633
$909$	−32464.2	−1.18456
$910$	0	0
$911$	−7316.34	−0.266083	−0.133041	−	0.991110i	$-0.542474\pi$
$911$	−7316.34	−0.266083	−0.133041	+	0.991110i	$0.542474\pi$
$912$	−21093.5	−0.765872
$913$	17723.9	0.642470
$914$	2672.34	0.0967104
$915$	−32044.9	−1.15778
$916$	−44328.2	−1.59896
$917$	0	0
$918$	−10101.4	−0.363175
$919$	−29717.6	−1.06670	−0.533348	−	0.845896i	$-0.679066\pi$
$919$	−29717.6	−1.06670	−0.533348	+	0.845896i	$0.679066\pi$
$920$	−8543.86	−0.306177
$921$	43280.7	1.54848
$922$	−72216.7	−2.57953
$923$	16049.8	0.572357
$924$	0	0
$925$	18405.8	0.654247
$926$	30223.1	1.07256
$927$	−8214.96	−0.291062
$928$	26084.7	0.922706
$929$	−13030.6	−0.460196	−0.230098	−	0.973168i	$-0.573905\pi$
$929$	−13030.6	−0.460196	−0.230098	+	0.973168i	$0.573905\pi$
$930$	15703.1	0.553681
$931$	0	0
$932$	−27428.7	−0.964009
$933$	32238.5	1.13124
$934$	6908.93	0.242042
$935$	−9627.17	−0.336729
$936$	12340.9	0.430957
$937$	51323.4	1.78939	0.894696	−	0.446675i	$-0.147392\pi$
$937$	51323.4	1.78939	0.894696	+	0.446675i	$0.147392\pi$
$938$	0	0
$939$	−74015.8	−2.57233
$940$	3486.13	0.120963
$941$	−22968.3	−0.795691	−0.397845	−	0.917452i	$-0.630242\pi$
$941$	−22968.3	−0.795691	−0.397845	+	0.917452i	$0.630242\pi$
$942$	−82108.6	−2.83996
$943$	87323.7	3.01554
$944$	−35863.2	−1.23649
$945$	0	0
$946$	−25681.7	−0.882648
$947$	−17631.5	−0.605013	−0.302506	−	0.953147i	$-0.597823\pi$
$947$	−17631.5	−0.605013	−0.302506	+	0.953147i	$0.597823\pi$
$948$	−1581.29	−0.0541752
$949$	−78814.1	−2.69591
$950$	12379.6	0.422787
$951$	−2682.28	−0.0914604
$952$	0	0
$953$	−4697.66	−0.159677	−0.0798386	−	0.996808i	$-0.525440\pi$
$953$	−4697.66	−0.159677	−0.0798386	+	0.996808i	$0.525440\pi$
$954$	−30516.5	−1.03565
$955$	19259.8	0.652600
$956$	52132.5	1.76369
$957$	−35940.5	−1.21399
$958$	7551.93	0.254689
$959$	0	0
$960$	−42494.3	−1.42864
$961$	−26396.5	−0.886056
$962$	−81112.0	−2.71846
$963$	10132.5	0.339060
$964$	4919.85	0.164375
$965$	−25584.3	−0.853459
$966$	0	0
$967$	41909.5	1.39371	0.696855	−	0.717212i	$-0.254582\pi$
$967$	41909.5	1.39371	0.696855	+	0.717212i	$0.254582\pi$
$968$	−3181.68	−0.105644
$969$	10800.2	0.358052
$970$	−7305.85	−0.241832
$971$	−43438.4	−1.43564	−0.717819	−	0.696229i	$-0.754860\pi$
$971$	−43438.4	−1.43564	−0.717819	+	0.696229i	$0.754860\pi$
$972$	−44975.5	−1.48415
$973$	0	0
$974$	44870.4	1.47612
$975$	31123.1	1.02229
$976$	26035.5	0.853870
$977$	42090.0	1.37828	0.689140	−	0.724628i	$-0.257989\pi$
$977$	42090.0	1.37828	0.689140	+	0.724628i	$0.257989\pi$
$978$	−5985.57	−0.195703
$979$	−13237.9	−0.432160
$980$	0	0
$981$	81539.7	2.65379
$982$	68831.3	2.23676
$983$	11980.2	0.388718	0.194359	−	0.980931i	$-0.437737\pi$
$983$	11980.2	0.388718	0.194359	+	0.980931i	$0.437737\pi$
$984$	−16955.6	−0.549313
$985$	11458.0	0.370643
$986$	−11274.2	−0.364141
$987$	0	0
$988$	−29207.2	−0.940491
$989$	−29367.8	−0.944227
$990$	56417.3	1.81117
$991$	12867.3	0.412456	0.206228	−	0.978504i	$-0.433881\pi$
$991$	12867.3	0.412456	0.206228	+	0.978504i	$0.433881\pi$
$992$	−15113.8	−0.483735
$993$	−44165.0	−1.41141
$994$	0	0
$995$	−23476.1	−0.747982
$996$	−29784.8	−0.947559
$997$	24242.3	0.770073	0.385037	−	0.922901i	$-0.374189\pi$
$997$	24242.3	0.770073	0.385037	+	0.922901i	$0.374189\pi$
$998$	−36167.6	−1.14716
$999$	−27521.6	−0.871616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.5	yes	35
7.6	odd	2		2303.4.a.g.1.5	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.5	✓	35	7.6	odd	2
2303.4.a.h.1.5	yes	35	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2303.a (trivial)

\(f(q)\)	\(=\)	\(q-4.14945 q^{2} +8.07223 q^{3} +9.21794 q^{4} +8.04659 q^{5} -33.4953 q^{6} -5.05376 q^{8} +38.1609 q^{9} +O(q^{10})\)	\(q-4.14945 q^{2} +8.07223 q^{3} +9.21794 q^{4} +8.04659 q^{5} -33.4953 q^{6} -5.05376 q^{8} +38.1609 q^{9} -33.3889 q^{10} -44.2783 q^{11} +74.4093 q^{12} -63.9904 q^{13} +64.9539 q^{15} -52.7732 q^{16} +27.0207 q^{17} -158.347 q^{18} +49.5156 q^{19} +74.1729 q^{20} +183.731 q^{22} +210.101 q^{23} -40.7951 q^{24} -60.2524 q^{25} +265.525 q^{26} +90.0935 q^{27} +100.554 q^{29} -269.523 q^{30} -58.2624 q^{31} +259.410 q^{32} -357.425 q^{33} -112.121 q^{34} +351.765 q^{36} -305.478 q^{37} -205.462 q^{38} -516.545 q^{39} -40.6655 q^{40} +415.627 q^{41} -139.779 q^{43} -408.154 q^{44} +307.065 q^{45} -871.803 q^{46} +47.0000 q^{47} -425.997 q^{48} +250.015 q^{50} +218.117 q^{51} -589.859 q^{52} +192.720 q^{53} -373.838 q^{54} -356.289 q^{55} +399.701 q^{57} -417.244 q^{58} +679.573 q^{59} +598.741 q^{60} -493.348 q^{61} +241.757 q^{62} -654.222 q^{64} -514.904 q^{65} +1483.12 q^{66} +14.9318 q^{67} +249.075 q^{68} +1695.98 q^{69} -250.816 q^{71} -192.856 q^{72} +1231.66 q^{73} +1267.57 q^{74} -486.372 q^{75} +456.431 q^{76} +2143.38 q^{78} -21.2513 q^{79} -424.644 q^{80} -303.089 q^{81} -1724.63 q^{82} -400.284 q^{83} +217.424 q^{85} +580.007 q^{86} +811.695 q^{87} +223.772 q^{88} +298.970 q^{89} -1274.15 q^{90} +1936.70 q^{92} -470.308 q^{93} -195.024 q^{94} +398.431 q^{95} +2094.01 q^{96} +218.811 q^{97} -1689.70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Introduction

L-functions

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Database

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